{"id":298,"date":"2022-01-19T09:34:42","date_gmt":"2022-01-19T08:34:42","guid":{"rendered":"http:\/\/e-biostat.uniag.sk\/?p=298"},"modified":"2022-05-10T15:58:50","modified_gmt":"2022-05-10T13:58:50","slug":"distribucna-analyza","status":"publish","type":"post","link":"https:\/\/e-biostat.uniag.sk\/?p=298","title":{"rendered":"Distribu\u010dn\u00e1 anal\u00fdza"},"content":{"rendered":"\n

Norm\u00e1lne rozdelenie<\/strong><\/p>\n\n\n\n

V\u00e4\u010d\u0161ina \u0161tatistick\u00fdch anal\u00fdz a met\u00f3d predpoklad\u00e1, \u017ee \u00fadaje, ktor\u00e9 analyzujeme maj\u00fa norm\u00e1lne rozdelenie. Pred, alebo v r\u00e1mci skoro ka\u017edej anal\u00fdzy, overujeme \u010dasto predpoklad norm\u00e1lneho rozdelenia po\u010detnosti jednotliv\u00fdch vlastnost\u00ed a znakov. Normalita sa overuje na \u00farovni cel\u00e9ho v\u00fdberov\u00e9ho s\u00faboru \u00fadajov, alebo v r\u00e1mci jednotliv\u00fdch trieden\u00ed znakov (v r\u00e1mci definovan\u00fdch skup\u00edn hodnoten\u00e9ho \u00fadajov\u00e9ho s\u00faboru).
<\/p>\n\n\n\n

Existuje nieko\u013eko naj\u010dastej\u0161ie pou\u017e\u00edvan\u00fdch sp\u00f4sobov, ako skontrolova\u0165 normalitu rozdelenia po\u010detnosti:<\/strong>
<\/p>\n\n\n\n

\u2022 grafick\u00e9 zostavenie histogramov s jednoduch\u00fdm vizu\u00e1lnym pos\u00faden\u00edm normality (\u010dasto vyu\u017e\u00edvan\u00e9 pri anal\u00fdze biologick\u00fdch \u00fadajov),
\u2022 v\u00fdpo\u010det \u0161ikmosti (koeficient \u0161ikmosti je v skuto\u010dnosti mierou asymetrie rozlo\u017eenia po\u010detnosti, ak je hodnota koeficienta \u0161ikmosti bl\u00edzka \u010d\u00edslu 0,znamen\u00e1 to, \u017ee \u00fadaje s\u00fa s najv\u00e4\u010d\u0161ou pravdepodobnos\u0165ou norm\u00e1lne,
\u2022 numerick\u00e9 testy normality \u00fadajov<\/p>\n\n\n\n

Pozit\u00edvne skreslenie \u00fadajov znamen\u00e1, \u017ee existuje nieko\u013eko extr\u00e9mne ve\u013ek\u00fdch hodn\u00f4t, ktor\u00e9 menia svoj priemer na kladn\u00e9 skreslenie. Naz\u00fdva sa tie\u017e vpravo skosen\u00fd (positive skewness) : Ak je \u0161ikmos\u0165 > 0, \u00fadaje s\u00fa pozit\u00edvne skreslen\u00e9. \u010eal\u0161\u00ed sp\u00f4sob, ako vidie\u0165 pozit\u00edvnu \u0161ikmos\u0165: Priemer je v\u00e4\u010d\u0161\u00ed ako medi\u00e1n a medi\u00e1n je v\u00e4\u010d\u0161\u00ed ako re\u017eim. Negat\u00edvne skreslen\u00e9 \u00fadaje znamenaj\u00fa, \u017ee existuje nieko\u013eko extr\u00e9mne mal\u00fdch hodn\u00f4t, ktor\u00e9 menia svoj priemer na negat\u00edvne skreslenie. Naz\u00fdva sa tie\u017e v\u013eavo skosen\u00fd (negative skewness) : Ak je \u0161ikmos\u0165 < 0, \u00fadaje s\u00fa negat\u00edvne skreslen\u00e9. \u010eal\u0161\u00ed sp\u00f4sob, ako vidie\u0165 negat\u00edvnu \u0161ikmos\u0165: Priemer je men\u0161\u00ed ako medi\u00e1n a medi\u00e1n je men\u0161\u00ed ako modus. Ak je \u0161ikmos\u0165 < -1 alebo > +1, distrib\u00facia je ve\u013emi skreslen\u00e1. Ak je \u0161ikmos\u0165 medzi -1 a -0,5 alebo medzi 0,5 a +1, distrib\u00facia je mierne skreslen\u00e1. Ak je \u0161ikmos\u0165 > -0,5 a < 0,5, rozdelenie je pribli\u017ene symetrick\u00e9 alebo norm\u00e1lne.<\/p>\n\n\n\n

Uv\u00e1dzame dva hlavn\u00e9 testy normality:<\/p>\n\n\n\n

  1. Shapiro Wilk test (ve\u013ekos\u0165 vzorky <= 2000)
    Nulov\u00e1 hypot\u00e9za uv\u00e1dza, \u017ee rozdelenie je norm\u00e1lne.
    Ak je hodnota p men\u0161ia ako 0,05 tak nulov\u00fa hypot\u00e9zu zamietame. Znamen\u00e1 to, \u017ee distrib\u00facia nie je norm\u00e1lna. Ak je p-hodnota > 0,05, znamen\u00e1 to, \u017ee rozdelenie je norm\u00e1lne. Tento test funguje dobre v malej vzorke do 2000 pozorovan\u00ed.<\/li><\/ol>\n\n\n\n
    1. Kolmogorov-Smirnovov test (ve\u013ekos\u0165 vzorky > 2000)
      V tomto teste nulov\u00e1 hypot\u00e9za uv\u00e1dza, \u017ee \u00fadaje s\u00fa norm\u00e1lne rozdelen\u00e9.
      Ak je p-hodnota > 0,05, \u00fadaje s\u00fa norm\u00e1lne. Rovnako aj v tomto pr\u00edpade ak je p-hodnota men\u0161ia ako 0,05, \u00fadaje nie s\u00fa norm\u00e1lne. Test sa naj\u010dastej\u0161ie vyu\u017e\u00edva vo vzork\u00e1ch \u00fadajov v\u00e4\u010d\u0161\u00edch ako 2000 pozorovan\u00ed.<\/li><\/ol>\n\n\n\n

      Vzorov\u00e9 \u00fadaje (zdroj: Datab\u00e1za \u00fadajov projektu KEGA)<\/strong><\/p>\n\n\n\n

      \u00dadaje predstavuj\u00fa z\u00e1znamy mliekovej \u00fa\u017eitkovosti kr\u00e1v hol\u0161tajnsk\u00e9ho plemena (denn\u00e9 kontroln\u00e9 n\u00e1doje) spolu s po\u010dtom somatick\u00fdch buniek v kravskom mlieku.<\/p>\n\n\n\n

      \"\"<\/figure><\/div>\n\n\n\n

      Pr\u00edklad 1.3.1 <\/strong><\/p>\n\n\n\n

      Zistite \u010di ukazovate\u013e denn\u00fd n\u00e1doj mlieka v kilogramoch (Mlieko) a ukazovate\u013e somatick\u00e9 bunky (SB) maj\u00fa norm\u00e1lne rozdelenie po\u010detnosti. V pr\u00edpade \u017ee niektor\u00fd s ukazovate\u013eov nem\u00e1 norm\u00e1lne rozdelenie po\u010detnosti uskuto\u010dnite logaritmick\u00fa transform\u00e1ciu (normaliz\u00e1ciu) ukazovate\u013ea.<\/p>\n\n\n\n

      V\u00fdsledky distribu\u010dnej anal\u00fdzy<\/strong> (program SAS) – ukazovate\u013e mlieko<\/p>\n\n\n\n

      \"\"<\/figure><\/div>\n\n\n\n

      Testy normality<\/strong><\/p>\n\n\n\n

      \"\"<\/figure><\/div>\n\n\n\n

      Testy normality jednozna\u010dne potvrdili, \u017ee ukazovate\u013e mlieko m\u00e1 norm\u00e1lne rozdelenie po\u010detnosti (hodnoty p > 0,05).<\/p>\n\n\n\n

      \"\"<\/figure><\/div>\n\n\n\n

      Na z\u00e1klade grafick\u00e9ho zn\u00e1zornenia distribu\u010dnej anal\u00fdzy m\u00f4\u017eeme kon\u0161tatova\u0165, \u017ee hodnoten\u00fd ukazovate\u013e Mlieko m\u00e1 norm\u00e1lne rozdelenie. Potvrdzuje to aj graf pravdepodobnosti normality percent\u00edl. Jednotliv\u00e9 body le\u017eia v pribli\u017enej priamke, \u010do nazna\u010duje, \u017ee \u00fadaje s\u00fa s najv\u00e4\u010d\u0161ou pravdepodobnos\u0165ou norm\u00e1lne rozlo\u017een\u00e9.<\/p>\n\n\n\n

      V\u00fdsledky distribu\u010dnej anal\u00fdzy<\/strong> (program SAS) – ukazovate\u013e po\u010det somatick\u00fdch buniek <\/p>\n\n\n\n

      \"\"<\/figure><\/div>\n\n\n\n

      U\u017e z\u00e1klade z\u00e1kladn\u00fdch \u0161tatistick\u00fdch charakterist\u00edk sa d\u00e1 predpoklada\u0165, \u017ee ukazovate\u013e nem\u00e1 norm\u00e1lne rozdelenie (koeficient \u0161ikmosti dosahuje hodnotu 3,73).<\/p>\n\n\n\n

      Grafick\u00e9 zn\u00e1zornenie rozdelenia po\u010detnosti ukazovate\u013ea po\u010det somatick\u00fdch buniek<\/strong><\/p>\n\n\n\n

      \"\"<\/figure><\/div>\n\n\n\n

      Histogram aj graf pravdepodobnosti percent\u00edl ukazuj\u00fa, \u017ee ukazovate\u013e po\u010det somatick\u00fdch buniek nem\u00e1 norm\u00e1lne rozdelenie.<\/p>\n\n\n\n

      Testy normality<\/strong><\/p>\n\n\n\n

      \"\"<\/figure><\/div>\n\n\n\n

      Testy normality potvrdzuj\u00fa rovnak\u00fd v\u00fdsledok, ktor\u00fd iba dokazuje v\u00fdrazn\u00fa odli\u0161nos\u0165 rozdelenia po\u010detnosti od norm\u00e1lneho rozdelenia.<\/p>\n\n\n\n

      Postup transform\u00e1cie (normaliz\u00e1cie) ukazovate\u013ea po\u010det somatick\u00fdch buniek<\/strong><\/p>\n\n\n\n

      Jednou z mo\u017enost\u00ed transform\u00e1cie ukazovate\u013eov, ktor\u00e9 nemaj\u00fa norm\u00e1lne rozdelenie, je \u010dasto kr\u00e1t pou\u017e\u00edvan\u00e1 logaritmick\u00e1 transform\u00e1cia \u00fadajov. Program SAS poskytuje mo\u017enosti ve\u013emi efekt\u00edvnej automatickej logaritmickej transform\u00e1cie. Pre transform\u00e1ciu \u00fadajov sme pou\u017eili transform\u00e1ciu na tzv. norm\u00e1lne sk\u00f3re (Blom formula, vzorec). Transform\u00e1ciou sa p\u00f4vodn\u00fd hodnoten\u00fd s\u00fabor \u00fadajov roz\u0161\u00edri o nov\u00fd ukazovate\u013e, ktor\u00fd n\u00e1sledne m\u00f4\u017eeme pou\u017ei\u0165 pri opakovanej distribu\u010dnej anal\u00fdze, aby sme overili, \u010di uskuto\u010dnen\u00e1 transform\u00e1cia \u00fadajov bola \u00faspe\u0161n\u00e1. Uveden\u00fd postup transform\u00e1cie sa d\u00e1 ale po\u017ei\u0165 aj prepo\u010dtom ukazovate\u013ea po\u010det somatick\u00fdch buniek pod\u013ea vhodne zvolen\u00e9ho logaritmick\u00e9ho vzorca. V pr\u00edpade hodnotenia somatick\u00fdch buniek v r\u00e1mci kontroly mliekovej \u00fa\u017eitkovosti hov\u00e4dzieho dobytka v Slovenskej republike sa pou\u017e\u00edva pr\u00e1ve tak\u00fdto postup. Vyu\u017e\u00edva sa nasledovn\u00fd vzorec na prepo\u010det na sk\u00f3re za somatick\u00e9 bunky: sk\u00f3re = ln (SB\/100)+3 (po\u017eit\u00fd prirodzen\u00fd logaritmus).<\/p>\n\n\n\n

      V\u00fdsledky distribu\u010dnej anal\u00fdzy<\/strong> (program SAS) – transformovan\u00fd ukazovate\u013e sk\u00f3re za somatick\u00e9 bunky <\/p>\n\n\n\n

      \"\"<\/figure><\/div>\n\n\n\n

      Grafick\u00e9 zn\u00e1zornenie rozdelenia po\u010detnosti ukazovate\u013ea sk\u00f3re za po\u010det somatick\u00fdch buniek<\/strong><\/p>\n\n\n\n

      \"\"<\/figure><\/div>\n\n\n\n

      Grafick\u00e9 zobrazenia ukazuj\u00fa jednozna\u010dne, \u017ee transformovan\u00fd po\u010det somatick\u00fdch buniek m\u00e1 priam ide\u00e1lne norm\u00e1lne rozdelenie po\u010detnosti.<\/p>\n\n\n\n

      Testy normality<\/strong> <\/p>\n\n\n\n

      \"\"<\/figure><\/div>\n\n\n\n

      Norm\u00e1lne rozdelenie po\u010detnosti pre transformovan\u00fd po\u010det somatick\u00fdch buniek potvrdzuj\u00fa aj jednotliv\u00e9 testy normality (p hodnoty s\u00fa v\u00fdrazne v\u00e4\u010d\u0161ie ako je definovan\u00e1 hrani\u010dn\u00e1 hodnota 0,05).<\/p>\n\n\n\n

      Praktick\u00e9 pou\u017eitie programu R (R Studio)<\/strong><\/p>\n\n\n\n

           Pr\u00edklad 1.9 (Program R)<\/strong><\/p>\n\n\n\n

                  Zistite \u010di ukazovate\u013e denn\u00fd n\u00e1doj mlieka v kilogramoch (Mlieko) a ukazovate\u013e somatick\u00e9 bunky (SB) maj\u00fa norm\u00e1lne rozdelenie po\u010detnosti. V pr\u00edpade \u017ee niektor\u00fd s ukazovate\u013eov nem\u00e1 norm\u00e1lne rozdelenie po\u010detnosti uskuto\u010dnite logaritmick\u00fa transform\u00e1ciu (normaliz\u00e1ciu) ukazovate\u013ea.<\/p>\n\n\n\n

      Zdrojov\u00fd k\u00f3d potrebn\u00fd na import a zobrazenie excelovsk\u00e9ho s\u00faboru „data_sb.xls“, ktor\u00fd je mo\u017en\u00e9 pou\u017ei\u0165 priamo v programe R, alebo R Studio ako s\u00fabor s n\u00e1zvom data_sb<\/strong>:<\/p>\n\n\n\n

      \"\"<\/figure><\/div>\n\n\n\n
      \"\"<\/figure><\/div>\n\n\n\n
      \"\"<\/figure><\/div>\n\n\n\n
      \"\"<\/figure><\/div>\n","protected":false},"excerpt":{"rendered":"

      Norm\u00e1lne rozdelenie V\u00e4\u010d\u0161ina \u0161tatistick\u00fdch anal\u00fdz a met\u00f3d predpoklad\u00e1, \u017ee \u00fadaje, ktor\u00e9 analyzujeme maj\u00fa norm\u00e1lne rozdelenie. Pred, alebo v r\u00e1mci skoro ka\u017edej anal\u00fdzy, overujeme \u010dasto predpoklad norm\u00e1lneho rozdelenia po\u010detnosti jednotliv\u00fdch vlastnost\u00ed […]<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"Layout":"1c-narrow"},"categories":[1],"tags":[],"_links":{"self":[{"href":"https:\/\/e-biostat.uniag.sk\/index.php?rest_route=\/wp\/v2\/posts\/298"}],"collection":[{"href":"https:\/\/e-biostat.uniag.sk\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/e-biostat.uniag.sk\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/e-biostat.uniag.sk\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/e-biostat.uniag.sk\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=298"}],"version-history":[{"count":25,"href":"https:\/\/e-biostat.uniag.sk\/index.php?rest_route=\/wp\/v2\/posts\/298\/revisions"}],"predecessor-version":[{"id":680,"href":"https:\/\/e-biostat.uniag.sk\/index.php?rest_route=\/wp\/v2\/posts\/298\/revisions\/680"}],"wp:attachment":[{"href":"https:\/\/e-biostat.uniag.sk\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=298"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/e-biostat.uniag.sk\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=298"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/e-biostat.uniag.sk\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=298"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}